With no offense intended (because the fault is on the cabinet maker), that’s one of the flimsiest looking designs I’ve seen. In most cases, the face is just a plate attached to the cabinet itself.
As for fixing it, it looks like it was just stapled through the sides. I’d pull the staples and clean up the bits where the face ripped off. Maybe try filling in those parts of the face plate with some wood fill or bondo. Then you can run some glue along the cabinet and glue the face back on. Maybe run some L-brackets and nails/screws into it, too, if it still feels flimsy.